1. Field of the Invention
The present invention relates in general to object modeling, and in particular to a system and method for computing rectifying homographies for stereo vision processing of three dimensional (3D) objects.
2. Related Art
In the stereo computer vision field, it is typically assumed that a pair of two dimensional (2D) images of a three dimensional (3D) object or environment are taken from two distinct viewpoints. For certain stereo vision computations, the epipolar geometry of the two images is usually determined first and corresponding points between the two images typically need to satisfy an epipolar constraint. Next, for a given point in one image, a search is initiated for its correspondence in the other image along an epipolar line. In general, epipolar lines are not aligned with coordinate axis and are not parallel.
However, such searches are time consuming since the pixels of each image are compared on skewed lines in image space. These types of computations can be simplified and made more efficient if epipolar lines are axis aligned and parallel. This can be realized by applying 2D projective transforms, or homographies, to each image. This process is known as image rectification. In general, image rectification involves applying a pair of two dimensional (2D) projective transforms, or homographies, to a pair of images whose epipolar geometry is known so that epipolar lines in the original images map to horizontally aligned lines in the transformed images.
The pixels corresponding to point features from a rectified image pair will lie on the same horizontal scan-line and differ only in horizontal displacement. This horizontal displacement or disparity between rectified feature points is related to the depth of the feature. As such, rectification can be used to recover 3D structure from an image pair without appealing to 3D geometry notions like cameras. Computations that find dense correspondences are based on correlating pixel colors along epipolar lines. Typically, distinct views of a scene can be morphed by linear interpolation along rectified scan-lines to produce new geometrically correct views of the scene. Thus, image rectification is an important component of stereo computer vision computations and processing.
Some previous techniques for finding image rectification homographies involve 3D constructions. These methods find the 3D line of intersection between image planes and project the two images onto a plane containing this line that is parallel to the line joining the optical centers. However, its realization in practice is difficult because it involves 3D geometric construction. Although a 2D approach exists, it does not optimally reduce distortion effects of image rectification. Instead, the distortion minimization criterion is based on a simple geometric heuristic, which may not lead to optimal solutions.
Therefore, what is needed is an efficient system and method for computing rectifying homographies of 2D images of a 3D object for stereo vision processing of the 3D objects. What is also needed is a system and method that rectifies images with optimally reduced distortion.
Whatever the merits of the above mentioned systems and methods, they do not achieve the benefits of the present invention.
To overcome the limitations in the prior art described above, and to overcome other limitations that will become apparent upon reading and understanding the present specification, the present invention is embodied in a system and method for computing rectifying homographies for stereo vision processing of three dimensional (3D) objects.
In general, the system and method of the present invention computes 2D projective transforms or homographies derived from specialized projective and affine transforms or components. The affine transform is comprised of a similarity transform and an optional shearing transform for image rectification. During image rectification of the present invention, optimization techniques are used for reducing the distortion.
Namely, first, two-dimensional (2D) images of a three-dimensional (3D) object are obtained. Next, a fundamental matrix between the two images is obtained. The fundamental matrix embodies the epipolar geometry between the images. For each image, a special projective transform is then found that minimizes a well defined projective distortion criteria. Next, for each image, an affine transform is computed. The affine transform is comprised of a similarity and an optional shearing transform.
The similarity transform is found such that it satisfies the constraints for rectification. The shearing transform can be found for further reducing distortion introduced by the projective component. The similarity and optional shearing transforms are combined into a final affine component for each homography. Next, for each homography, the special projective and final affine transforms are combined into the rectifying homography. With the use of the above transforms of the present invention, rectification of each image is produced with minimum distortion.
The present invention as well as a more complete understanding thereof will be made apparent from a study of the following detailed description of the invention in connection with the accompanying drawings and appended claims.